7755501
Description
Flashcards by Lance Erickson, updated more than 1 year ago
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Created by Lance Erickson
almost 8 years ago
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| Question | Answer |
| The ml of oil in a tank as a function of time, x, in seconds is given. What is the minimum amount of oil in the tank? | you need the y coordinate of the vertex. start with x = -b/2a then sub. into f(x) for y coordinate. |
| The ml of oil in a tank as a function of time, x, in seconds is given. What time will the tank have 100 ml of oil? | sub. 100 into f(x) then solve. since you have x^2 and x you need to use formula (try factor). first step is get " = 0" |
| The ml of oil in a tank as a function of time, x, in seconds is given. How much oil is in the tank after 1 minute? | you need to substitute into x. however, first convert 1 minute into seconds. so put 60 into x and calculate. |
| Solve for x. | since you have x^2 and x you need to use formula (try factor). first step is get " = 0" |
| solve for x | add 8 , divide by 2, square root +/- then add 3 |
| solve for x. | no work to do. x = 1 and - 1/2 |
| find x intercepts | 0! put 0 into y to get above equation and solve |
| name all the things you can know from this equation. | 1) vertex is (3,-8) 2) range is [-8, infinity) 3) minimum is -8 4) line of symmetry is x = 3 5) f(x) is increasing (3 , infinity) and decreasing (- infinity , 3) |
| The point A(3,-2) is on f(x). what is the image of this point under this transformation? | h r s v so x minus 2, y times 3 and finally y minus 4 which gives: A'(1,-10) |
| what does this tell you? | 1) vertex is (-2, -4) 2) range is [-4, infinity) 3) minimum is -4 4) line of symmetry is x = - 2 5) f(x) is increasing (-2 , infinity) and decreasing (- infinity , -2) |
| convert to standard form. | First FOIL. Second distribute in 3. Third, collect like terms. Notice that "a" is the same in both. |
| solve for x. | you can not just "read" the answer. FOIL then get " = 0" then formula (factor if lucky) |
| solve for x. | Notice "= 0" so x = 0, x = -2, x = 7 |
| What does this tell you? | 1) vertex is (4, 2) 2) range is (-infinity, 2] 3) maximum is 2 4) line of symmetry is x = -4 5) f(x) is decreasing (4 , infinity) and increasing (- infinity , 4) |
| solve graphically | graph y = 0 and y = 3x(x+2)(x-7). Find the point(s) of intersection and take only the x coordinate. |
| solve for x. | solve then check intervals. to solve, answers are x = 0, x = -2 and x = 7 Check intervals: example let x = 1 then 3(1)(1+2)(1-7)= -54 < 0 so (0,7 ) is part of answer. |
| The point A(3,-2) is on f(x). what is the image of this point under this transformation? | h r s v y times -5 and x time 1/2 finally y plus 3 which gives: A'(3/2,13) |
| vertex? | start with x = -b/2a then sub. into f(x) for y coordinate. |
| line of symmetry? | you need the x coordinate of the vertex. x = -b/2a |
| solve by completing the square | 1) = 0 so move 5x - 1 2) move constant back to get -4 3) a= 1. move on. 4) add (b/2)^2 to both sides 5) factor and solve |
| what can you see from the function? | 1) should be 4 x intercepts 2) should be 3 turning points 3) right side goes up 4) y intercept is -3 |
| is this function odd, even or neither? | sub in -x and simplify. if the result is f(x) it is even. if it is the opposite of f(x) (i.e. -f(x) ) otherwise it is neither |
| simplify | 1 - (-1) + (-i) = 2 - i |
| simplify | use the conjugate 2 - 3i. final answer: 1/11 + 18i/11 please let me know if this is wrong. |
| find the equation for the parabola shown | put vertex into the equation and sub. in a point (0,3). y = - 2(x-1)^2 +5 |
| when do you need x = -b/2a? | if it is in standard form and you want: vertex or vertex form or line of symmetry or minimum/maximum or range or where increasing/decreasing |
| what can you say about the discriminate? | D > 0 since there are 2 x intercepts. If D = 0 there is only 1 intercept if D < 0 then there no intercepts and the solutions are imaginary. |
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